Lesson a: Vibrational Motion
What causes things to vibrate?
- Objects have resting positions (equilibrium position); when positioned at it's equilibrium position, the object is at equilibrium (has balanced forces)
- When a force is applied to the object, it can be displaced from its equilibrium position
- The force disturbs the equilibrium and causes the object to vibrate
- Some objects experience damping (when a vibrating object loses energy over time, ex: bobble head)
What is the restoring force?
- It is the force that acts upon the vibrating object to move it back to its original equilibrium position Lesson b: Properties of Periodic Motion
What is periodic motion?
- It is a motion that is regular and repeating (most objects vibrate this way)
- The graph is that of a sin function
- PERIOD= the time for the mass to complete a cycle; sec/cycle
- AMPLITUDE= the maximum displacement of the mass above or below the resting position
- FREQUENCY= the number of complete cycles occurring per period of time; cycle/sec Lesson c: Pendulum Motion
What is pendulum motion?
- An object must experience a resotring force to vibrate
- Hanging masses that swing back and forth move as a pendulum
What are the forces acting on a pendulum?
- The force of gravity is always directed downward (its magnitude never changes; 9.8)
- The tension force is always directed towards the pivot (its magnitude varies over the course of the vibration)
- Graph --> sin function
Lesson d: Motion of a Mass on a Spring
What is the motion of a mass on a spring?
- Use Hooke's Law (force= k*x)
- Graph--> sin function
- Period of mass on a spring:
Lesson 1: The Nature of a Wave
Lesson a: Waves and Wavelike Motion
Describe waves and their motion.
- The 2 most common types of waves are sound waves and light waves
- The motion of a pendulum, the motion of a mass suspended by a spring, and the motion of a child on a swing can be thought of as wavelike
- Waves can move together as a front in a straight-line direrction
- Or they can be circular that originate from a point where the disturbance occurred and travel in all directions Lesson b: What is a Wave?
What is a wave?
- It's a repeating and periodic disturbance that travels though a medium from one location to another
- A pulse is a single disturbance moving through a medium from one location to another
- A medium is a substance or material that carries a wave
- Waves transport energy and not matter Lesson c: Categories of Waves
What types of waves are there?
- Transverse wave: one in which particular particles of the mdium move in a direction perpendicular to the direction that the wave moves
- Longitudinal wave: one in which particles of the medium move in a direction parallel to the direction that the wave moves
- Surface wave: one in which particles of the medium undergo a circular motion
- Electromagnetic wave: one that is capable of transmitting its energy through a vacuum
- Mechanical wave: one that is NOT capable of transmitting its energy through a vacuum (ex: a sound wave)
May 7, 2012
Lesson 4: Standing Waves
a.) Traveling Waves vs. Standing Waves
What is the difference between a traveling and a standing wave?
- Mechanical wave= a disturbance created by a vibrating object that then goes through a medium from one point to another, transporting energy as it moves
- Traveling wave= when a wave is not confined to a given space along the medium (ex: ocean waves)
- Standing wave= when a wave is confined to a given space in a medium and still produces a regular wave pattern; it's characterized by points appear to be standing still b.) Formation of Standing Waves
Describe the formation of standing waves.
- Standing wave pattern= a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source
- Harmonics= these frequencies
- 2 pulses can interfere/ pass through each other c.) Nodes and Anti-nodes
What are nodes and anti- nodes?
- Nodes (N)= points along the medium that have no displacment
- Anti-Noes (AN)= points along the medium that vibrate back and forth between points of large positive and negative displacements d.) Harmonics and Patterns
Describe harmonic wave patterns.
- e.) Mathematics of Standing Waves
What is the mathematics of standing waves?
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Table of Contents
Lesson 0: Vibrations
Lesson a: Vibrational MotionWhat causes things to vibrate?
- Objects have resting positions (equilibrium position); when positioned at it's equilibrium position, the object is at equilibrium (has balanced forces)
- When a force is applied to the object, it can be displaced from its equilibrium position
- The force disturbs the equilibrium and causes the object to vibrate
- Some objects experience damping (when a vibrating object loses energy over time, ex: bobble head)
What is the restoring force?
- It is the force that acts upon the vibrating object to move it back to its original equilibrium position
Lesson b: Properties of Periodic Motion
What is periodic motion?
- It is a motion that is regular and repeating (most objects vibrate this way)
- The graph is that of a sin function
- PERIOD= the time for the mass to complete a cycle; sec/cycle
- AMPLITUDE= the maximum displacement of the mass above or below the resting position
- FREQUENCY= the number of complete cycles occurring per period of time; cycle/sec
Lesson c: Pendulum Motion
What is pendulum motion?
- An object must experience a resotring force to vibrate
- Hanging masses that swing back and forth move as a pendulum
What are the forces acting on a pendulum?
- The force of gravity is always directed downward (its magnitude never changes; 9.8)
- The tension force is always directed towards the pivot (its magnitude varies over the course of the vibration)
- Graph --> sin function
Lesson d: Motion of a Mass on a Spring
What is the motion of a mass on a spring?
- Use Hooke's Law (force= k*x)
- Graph--> sin function
- Period of mass on a spring:
Lesson 1: The Nature of a Wave
Lesson a: Waves and Wavelike MotionDescribe waves and their motion.
- The 2 most common types of waves are sound waves and light waves
- The motion of a pendulum, the motion of a mass suspended by a spring, and the motion of a child on a swing can be thought of as wavelike
- Waves can move together as a front in a straight-line direrction
- Or they can be circular that originate from a point where the disturbance occurred and travel in all directions
Lesson b: What is a Wave?
What is a wave?
- It's a repeating and periodic disturbance that travels though a medium from one location to another
- A pulse is a single disturbance moving through a medium from one location to another
- A medium is a substance or material that carries a wave
- Waves transport energy and not matter
Lesson c: Categories of Waves
What types of waves are there?
- Transverse wave: one in which particular particles of the mdium move in a direction perpendicular to the direction that the wave moves
- Longitudinal wave: one in which particles of the medium move in a direction parallel to the direction that the wave moves
- Surface wave: one in which particles of the medium undergo a circular motion
- Electromagnetic wave: one that is capable of transmitting its energy through a vacuum
- Mechanical wave: one that is NOT capable of transmitting its energy through a vacuum (ex: a sound wave)
May 7, 2012
Lesson 4: Standing Waves
a.) Traveling Waves vs. Standing WavesWhat is the difference between a traveling and a standing wave?
- Mechanical wave= a disturbance created by a vibrating object that then goes through a medium from one point to another, transporting energy as it moves
- Traveling wave= when a wave is not confined to a given space along the medium (ex: ocean waves)
- Standing wave= when a wave is confined to a given space in a medium and still produces a regular wave pattern; it's characterized by points appear to be standing still
b.) Formation of Standing Waves
Describe the formation of standing waves.
- Standing wave pattern= a vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source
- Harmonics= these frequencies
- 2 pulses can interfere/ pass through each other
c.) Nodes and Anti-nodes
What are nodes and anti- nodes?
- Nodes (N)= points along the medium that have no displacment
- Anti-Noes (AN)= points along the medium that vibrate back and forth between points of large positive and negative displacements
d.) Harmonics and Patterns
Describe harmonic wave patterns.
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e.) Mathematics of Standing Waves
What is the mathematics of standing waves?
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